We utilize advanced physical and mathematical methods to understand the biophysics of complex cellular processes. Phenomena under study include chemotactic gradient sensing in eucaryotic cells, the stochastic biogenesis of coated vesicles involved in endocytosis and other intracellular transport processes, and the structural organization of multicellular biofilms arising from the attachment of prokaryotes to surfaces in nutrient-rich environments. These studies are of interest to persons studying basic cell biological processes, but they also are relevant to disease processes and normal and abnormal tissue development. Each requires the integration of several complicated processes, utilizing information obtained through reductionist studies but here focusing on behaviors emerging from both synergistic and competitive interactions. [unreadable] [unreadable] Chemotaxis, i.e., the spatially-directed cell response to gradients of chemical signals, is an important element in such critical processes as wound healing, immune surveillance, tissue development, angiogenesis, and creating connections between nerve cells. The first step in these processes, namely, gradient detection, has long been a subject of active investigation. We have devised a mathematical model, based on nonlinear reaction-diffusion equations for concentrations of 3'-phosphoinositides, PI3-kinases, and PTEN phosphatases, that captures the three major behaviors of these quantities observed in the chemotactic response of Dictyostelium and neutrophils: establishment of cell polarity in shallow spatial gradients of stimulus; adaptation to changes in uniform background levels of signaling ligand; and the ability of a cell to rapidly follow movements of an excitatory chemical source. In contrast with other treatments of this problem, this study explicitly incorporates plausible biochemical mechanisms, allowing us to gain insights into how molecular processes mediate the response. A recent extension of our earlier work now has provided a way to infer the angle dependence of the sensitivity of an already-polarized cell relative to the location of the source, providing an explanation for the zig-zag motions that are occasionally observed when a neutrophil travels towards a target.[unreadable] [unreadable] In addition to their involvement in gradient sensing, 3' phosphoinositides are implicated in the biogenesis of clathrin-coated and other endocytic vesicles. We have constructed a complex, multi-element model of receptor mediated endocytosis that encompasses cargo recognition, phosphoinositide metabolism, and clathrin coat formation and dissolution. The analysis demonstrates how the inter-related kinetic elements of these processes determine whether an endocytic vesicle will form. Not only does the model explain how vesicle biogenesis is triggered by, e.g., the binding of ligands to receptors at specific sites, but it also can rationalize the observed probabilistic quality of cell response in the presence of a stimilus.[unreadable] [unreadable] A third area of complex systems biology currently under investigation in our laboratory pertains to bacterial biofilms. The latter are surface-attached communities of microorganisms that express a polymer coating--the extracellular polymeric substance (EPS)--that protects the attached bacterial colonies from antimicrobial agents. Biofilms are ubiquitous in the natural and technologically-modified worlds, yet little is really understood about their formation and viability; in human disease many bacterial pathogens form biofilms which resist destruction, causing great distress for patients who are unfortunate enough to be infected. We have focused on measuring the mechanical and transport properties of the EPS as a function of environmental parameters such as pH and externally-induced shear forces. One goal of this research is to identify factors that affect the flow of antibiotics within a biofilm and to understand how the EPS mediates the activity of immune cells. Another is to understand how the transport of nutrients and signaling molecules within a film is coupled to the spatially-heterogenous structures that develop, with a view towards understanding how various agents might mediate the growth of the bacteria. We also are investigating how biofilms, which are amenable to external manipulation, can serve as rudimentary models for studying the growth and regeneration of more complex cell communities. In order to characterize the mechanical properties of the EPS, we have developed methods involving atomic force microscopy the allow us to take into account the spatial heterogeneity of the colonies. We have found that the soft, hydrated EPS gel, which consists mainly of polysaccharides, proteins and nucleic acids that carry labile charges, softens and stiffens according to the proton concentration in the surrounding environment.